Cube of 371

A cube number is a value obtained by raising a number to the power of 3, or by multiplying the number by itself three times.

When you cube a positive number, the result is always positive.

When you cube a negative number, the result is always negative.

This is because a negative number by itself three times results in a negative number.

The cube of 371 can be written as 371³, which is the exponential form.

Or it can also be written in arithmetic form as 371 × 371 × 371.

In order to check whether a number is a cube number or not, we can use the following three methods, such as multiplication method, a factor formula (a³), or by using a calculator. These three methods will help kids to cube the numbers faster and easier without feeling confused or stuck while evaluating the answers.

• By Multiplication Method
   
• Using a Formula
   
• Using a Calculator

The multiplication method is a process in mathematics used to find the product of two numbers or quantities by combining them through repeated addition. It is a fundamental operation that forms the basis for more complex mathematical concepts.

Step 1: Write down the cube of the given number. 371³ = 371 × 371 × 371

Step 2: You get 51,236,611 as the answer. Hence, the cube of 371 is 51,236,611.

The formula \((a + b)³\) is a binomial formula for finding the cube of a number. The formula is expanded as \(a³ + 3a²b + 3ab² + b³\).

Step 1: Split the number 371 into two parts, as 300 and 71. Let a = 300 and b = 71, so a + b = 371

Step 2: Now, apply the formula \((a + b)³ = a³ + 3a²b + 3ab² + b³\)

Step 3: Calculate each term \(a³ = 300³\) \(3a²b = 3 × 300² × 71\) \(3ab² = 3 × 300 × 71²\) \(b³ = 71³\)

Step 4: Add all the terms together: \((a + b)³ = a³ + 3a²b + 3ab² + b³\) \((300 + 71)³ = 300³ + 3 × 300² × 71 + 3 × 300 × 71² + 71³\) \(371³ = 27,000,000 + 19,170,000 + 4,533,000 + 357,911\) \(371³ = 51,236,611\)

Step 5: Hence, the cube of 371 is 51,236,611.

To find the cube of 371 using a calculator, input the number 371 and use the cube function (if available) or multiply 371 × 371 × 371. This operation calculates the value of 371³, resulting in 51,236,611. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 3 followed by 7 and 1

Step 3: If the calculator has a cube function, press it to calculate 371³.

Step 4: If there is no cube function on the calculator, simply multiply 371 three times manually.

Step 5: The calculator will display 51,236,611.

• The cube of any even number is always even, while the cube of any odd number is always odd.
   
• The product of two or more perfect cube numbers is always a perfect cube.
   
• A perfect cube can always be expressed as the product of three identical groups of equal prime factors.

• Binomial Formula: It is an algebraic expression used to expand the powers of a number, written as \((a + b)^n\), where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number.
   
• Cube of a Number: Multiplying a number by itself three times is called the cube of a number.
   
• Exponential Form: It is a way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2, which equals 8.
   
• Perfect Cube: A number that can be expressed as the cube of an integer. For example, 27 is a perfect cube because it is 3 × 3 × 3.
   
• Cube Root: A number that must be multiplied by itself three times to equal a given number. For example, the cube root of 27 is 3.